Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
4544 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 725 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×D17 | C2 | semidirect |
| 2. C23×D68 | C2 | semidirect |
| 3. C23×C22⋊D17 | C2 | semidirect |
| 4. C2×#10587568 | C2 | direct (N × H) |
| 5. C22×#63227 | C2 | semidirect |
| 6. C22×C22⋊C4×C17 | C2 | semidirect |
| 11. C24×D17 | C22 | semidirect |
| 12. C24×D17 | C22 | semidirect |
| 13. C23×C4×C17 | C22 | semidirect |
| 15. C22×C22⋊D17 | C22 | semidirect |
| 16. C23×Dic17 | C22 | semidirect |
| 18. C22×D68 | C22 | semidirect |
| 19. C2×C22⋊C4×C17 | C22 | semidirect |
| 20. C2×#63227 | C22 | semidirect |
| 21. #10587568 | C22 | direct (N × H) |
| 23. C24×C17 | D4 | semidirect |
| 33. C23×D17 | D4 | semidirect |
| 35. C23×D17 | C23 | semidirect |
| 36. C23×D17 | C23 | semidirect |
| 38. C22×C4×C17 | C23 | semidirect |
| 40. C2×C22⋊D17 | C23 | semidirect |
| 42. C22×Dic17 | C23 | semidirect |
| 44. C2×D68 | C23 | semidirect |
| 45. C22⋊C4×C17 | C23 | semidirect |
| 46. #63227 | C23 | semidirect |
| 51. C23×C17 | C2×D4 | semidirect |
| 63. C22×D17 | C2×D4 | semidirect |
| 65. C22×D17 | C24 | semidirect |
| 67. C2×C4×C17 | C24 | semidirect |
| 70. C2×Dic17 | C24 | semidirect |
| 75. C22×C17 | #120 | semidirect |
| 78. C22×C17 | C22×D4 | semidirect |
| 87. C2×D17 | C22×D4 | semidirect |
| 95. C22×C22⋊C4 | D17 | semidirect |
| 97. C2×C17 | C2×#120 | semidirect |
| 113. C23×C4 | C2×D17 | semidirect |
| 116. C2×C22⋊C4 | C2×D17 | semidirect |
| 117. C17 | C22×#120 | semidirect |
| 130. C24 | D68 | semidirect |
| 140. C22×C4 | C22×D17 | semidirect |
| 142. C22⋊C4 | C22×D17 | semidirect |
| 158. C23 | C2×D68 | semidirect |
| 167. C2×C4 | C23×D17 | semidirect |
| 178. C22 | #10587568 | direct (N × H) |
| 180. C22 | C22×D68 | semidirect |
| 188. C2 | C2×#10587568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D17 | 2 |
| C23×D68 | 2 |
| C23×C22⋊D17 | 2 |
| C2×#10587568 | 2 |
| C22×#63227 | 2 |
| C22×C22⋊C4×C17 | 2 |
| C22×#120 | 17 |